Persistent Disagreement and Polarization in a Bayesian Setting

Nielsen, Michael; Stewart, Rush T.

doi:10.1093/bjps/axy056

Cited by 18 publications

(18 citation statements)

References 44 publications

(36 reference statements)

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“…where A 0 = {ω ∈ Ω : P 1 (ω) > P 2 (ω)} (e.g., Nielsen and Stewart, 2021). So we take it that for global uncertainty to grow with respect to each cell of an experimental partition is for the total variation to increase conditional on each cell.…”

Section: Distentionmentioning

confidence: 99%

“…Local and global polarization are logically independent. While probabilities can exhibit local and global polarization simultaneously, global polarization does not imply local polarization, nor does local polarization imply global polarization (Nielsen and Stewart, 2021, Proposition 1). As we saw above, the IP analogues of local and global polarization, dilation and distention, respectively, exhibit the same sort of logical independence.…”

Section: Local and Global Polarizationmentioning

confidence: 99%

“…Another motivation for investigating distention comes from social epistemology. In Nielsen and Stewart (2021), we introduce the notions of local and global probabilistic opinion polarization between agents. There, we note 1) that the dilation phenomenon for imprecise probabilities is in some ways analogous to local polarization, and 2) that local and global polarization are logically independent.…”

Section: Introductionmentioning

confidence: 99%

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Distention for Sets of Probabilities

Stewart¹,

Nielsen

2022

Philos. sci.

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Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We investigate the short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging.

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Section: Distentionmentioning

confidence: 99%

Section: Local and Global Polarizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Distention for Sets of Probabilities

Stewart¹,

Nielsen

2022

Philos. sci.

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“…Then, divergent contrary updating, or belief polarisation, happens when Alice starts with a lower prior, and revises downwards ( H A < 0, likelihood ratio greater than one), whilst Bob starts with a higher prior and revises upwards ( H B > 0, likelihood ratio less than one), or vice versa, switching roles for Alice and Bob. That is, belief polarisation occurs either when l B < 1 < l A and h A ≤ h B or when l A < 1 < l B and h B ≤ h A (Jern et al 2014;Nielsen and Stewart 2019). This is a general criterion which applies not only when E and H are the only variables under consideration, but also in the more typical situation where the agents have probabilistic opinions about other variables as well.…”

Section: Belief Polarisation In a Bayesian Contextmentioning

confidence: 99%

The role of source reliability in belief polarisation

Henderson

Gebharter

2021

Synthese

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Psychological studies show that the beliefs of two agents in a hypothesis can diverge even if both agents receive the same evidence. This phenomenon of belief polarisation is often explained by invoking biased assimilation of evidence, where the agents’ prior views about the hypothesis affect the way they process the evidence. We suggest, using a Bayesian model, that even if such influence is excluded, belief polarisation can still arise by another mechanism. This alternative mechanism involves differential weighting of the evidence arising when agents have different initial views about the reliability of their sources of evidence. We provide a systematic exploration of the conditions for belief polarisation in Bayesian models which incorporate opinions about source reliability, and we discuss some implications of our findings for the psychological literature.

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“…Acemoglu, Chernozhukov, and Yildiz (2009) consider a Bayesian learning problem for agents with different priors about the distribution of signals and show that even a tiny amount of signal uncertainty leads to significant disagreement in asymptotic beliefs. 5 More recently, Nielsen and Stewart (2020) show that polarization can occur in a Bayesian setting where two rational agents learn a finite amount of shared evidence. In contrast to this literature, our analysis is about the polarization of observed actions resulting from the strategic incentives of agents rather than opinions or beliefs.…”

Section: Related Researchmentioning

confidence: 99%

Strategic Polarization in Group Interactions

Iyer¹,

Yoganarasimhan²

2021

Journal of Marketing Research

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We study the phenomenon of strategic group polarization in which members take more extreme actions than their preferences. The analysis is relevant for a broad range of formal and informal group settings, including social media, online platforms, sales teams, corporate and academic committees, and political action committees. In our model, agents with private preferences choose a public action (voice opinions), and the mean of their actions represents the group’s realized outcome. They face a trade-off between influencing the group decision and truth-telling. In a simultaneous move game, agents strategically shade their actions towards the extreme. The strategic group influence motive can create substantial polarization in actions and group decisions even when the preferences are relatively moderate. Compared to a simultaneous game, a randomized sequential actions game lowers polarization when agents’ preferences are relatively similar. Sequential actions can even lead to moderation if the later agents have moderate preferences. Endogenizing the order of moves (through a first-price sealed-bid auction) always increases polarization, but it is also welfare enhancing. Our findings can help group leaders, firms, and platforms design mechanisms that moderate polarization, e.g., the choice of speaking order, the group size, and the knowledge members have of others’ preferences and actions.

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Persistent Disagreement and Polarization in a Bayesian Setting

Cited by 18 publications

References 44 publications

Distention for Sets of Probabilities

Distention for Sets of Probabilities

The role of source reliability in belief polarisation

Strategic Polarization in Group Interactions

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